In a binary tree, what is the maximum number of leaf nodes?
Practice Questions
1 question
Q1
In a binary tree, what is the maximum number of leaf nodes?
n
n/2
2^(h-1)
2^h
In a binary tree of height h, the maximum number of leaf nodes is 2^(h-1), which occurs in a complete binary tree.
Questions & Step-by-step Solutions
1 item
Q
Q: In a binary tree, what is the maximum number of leaf nodes?
Solution: In a binary tree of height h, the maximum number of leaf nodes is 2^(h-1), which occurs in a complete binary tree.
Steps: 6
Step 1: Understand what a binary tree is. A binary tree is a tree data structure where each node has at most two children, referred to as the left child and the right child.
Step 2: Know what height means. The height of a binary tree is the number of edges on the longest path from the root node to a leaf node.
Step 3: Identify what leaf nodes are. Leaf nodes are the nodes in a binary tree that do not have any children (they are at the bottom of the tree).
Step 4: Learn about complete binary trees. A complete binary tree is a type of binary tree where all levels are fully filled except possibly for the last level, which is filled from left to right.
Step 5: Calculate the maximum number of leaf nodes. In a complete binary tree of height h, the maximum number of leaf nodes is 2^(h-1). This is because each level of the tree can have twice as many nodes as the level above it.
Step 6: Conclude that the formula 2^(h-1) gives you the maximum number of leaf nodes in a binary tree of height h.
